Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters

TL;DR

This paper presents a new framework for supervised labeled graph prediction using Fused Gromov-Wasserstein barycenters, combining theoretical guarantees with practical neural network models.

Contribution

It introduces a novel FGW barycenter-based regression framework with both non-parametric and neural network models, advancing graph prediction methods.

Findings

The non-parametric estimator is consistent with proven excess risk bounds.

The neural network model effectively learns barycenter weights and graphs, improving prediction.

The method performs well on simulated and real metabolic data with minimal engineering.

Abstract

This paper introduces a novel and generic framework to solve the flagship task of supervised labeled graph prediction by leveraging Optimal Transport tools. We formulate the problem as regression with the Fused Gromov-Wasserstein (FGW) loss and propose a predictive model relying on a FGW barycenter whose weights depend on inputs. First we introduce a non-parametric estimator based on kernel ridge regression for which theoretical results such as consistency and excess risk bound are proved. Next we propose an interpretable parametric model where the barycenter weights are modeled with a neural network and the graphs on which the FGW barycenter is calculated are additionally learned. Numerical experiments show the strength of the method and its ability to interpolate in the labeled graph space on simulated data and on a difficult metabolic identification problem where it can reach very good performance with very little engineering.